Homework 7–Qingqing

library(tidyverse)

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library(lubridate)

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##     date

Question 1. For the Water Years 2005-2012, develop a predictive model of the mean monthly Chl-a concentration in the California Bay Delta using other mean monthly water quality variables.

Step 1: get my desired dataset

BayDeltaWQ <- read.csv("BayDeltaWQ.csv")
BayDeltaWQ

names(BayDeltaWQ)

##   [1] "X"                                  
##   [2] "SampleDate"                         
##   [3] "StationCode"                        
##   [4] "Depth"                              
##   [5] "X1..Light.Depth"                    
##   [6] "Conductance..EC."                   
##   [7] "SiteDepth"                          
##   [8] "Field.Notes"                        
##   [9] "Fluorescence"                       
##  [10] "Latitude"                           
##  [11] "Longitude"                          
##  [12] "Oxygen"                             
##  [13] "pH"                                 
##  [14] "Secchi.Depth"                       
##  [15] "Temperature"                        
##  [16] "Tide.Stage"                         
##  [17] "Tide.Time"                          
##  [18] "Turbidity"                          
##  [19] "Weather.Observations"               
##  [20] "Wind.Direction"                     
##  [21] "Wind.Velocity"                      
##  [22] "VarType"                            
##  [23] "Alachlor"                           
##  [24] "Aldrin"                             
##  [25] "Ammonia..Dissolved."                
##  [26] "Ammonia..Total."                    
##  [27] "Arsenic..Dissolved."                
##  [28] "Arsenic..Total."                    
##  [29] "Atra.Simazine..Atrazine...Simazine."
##  [30] "Atrazine"                           
##  [31] "BHC"                                
##  [32] "BHC.alpha"                          
##  [33] "BHC.beta"                           
##  [34] "BHC.delta"                          
##  [35] "BHC.gamma..Lindane."                
##  [36] "Biochemical.Oxygen.Demand..BOD."    
##  [37] "Cadmium..Dissolved."                
##  [38] "Cadmium..Total."                    
##  [39] "Calcium..Dissolved."                
##  [40] "Captafol"                           
##  [41] "Captan"                             
##  [42] "Chlordane"                          
##  [43] "Chloride..Dissolved."               
##  [44] "Chloride..Total."                   
##  [45] "Chlorophyll.a"                      
##  [46] "Chlorothalonil"                     
##  [47] "Chlorpropham"                       
##  [48] "Chlorpyrifos"                       
##  [49] "Chromium..Dissolved."               
##  [50] "Chromium..Total."                   
##  [51] "Copper..Dissolved."                 
##  [52] "Copper..Total."                     
##  [53] "Dacthal..DCPA."                     
##  [54] "Dichloran"                          
##  [55] "Dicofol"                            
##  [56] "Dieldrin"                           
##  [57] "Diuron"                             
##  [58] "Endosulfan..mixed.isomers."         
##  [59] "Endosulfan.I"                       
##  [60] "Endosulfan.II"                      
##  [61] "Endrin"                             
##  [62] "Endrin.aldehyde"                    
##  [63] "Heptachlor"                         
##  [64] "Iron..Dissolved."                   
##  [65] "Iron..Total."                       
##  [66] "Kjeldahl.Nitrogen..Total."          
##  [67] "Lead..Dissolved."                   
##  [68] "Lead..Total."                       
##  [69] "Manganese..Dissolved."              
##  [70] "Manganese..Total."                  
##  [71] "Mercury..Total."                    
##  [72] "Methoxychlor"                       
##  [73] "Nitrate..Dissolved."                
##  [74] "Nitrite..Dissolved."                
##  [75] "Nitrite...Nitrate..Dissolved."      
##  [76] "Organic.Carbon..Dissolved."         
##  [77] "Organic.Carbon..Total."             
##  [78] "Organic.Nitrogen..Dissolved."       
##  [79] "Organic.Nitrogen..Total."           
##  [80] "Ortho.phosphate..Dissolved."        
##  [81] "p.p..DDD"                           
##  [82] "p.p..DDE"                           
##  [83] "p.p..DDT"                           
##  [84] "PCB.1016"                           
##  [85] "PCB.1221"                           
##  [86] "PCB.1232"                           
##  [87] "PCB.1242"                           
##  [88] "PCB.1248"                           
##  [89] "PCB.1254"                           
##  [90] "PCB.1260"                           
##  [91] "Pentachloronitrobenzene..PCNB."     
##  [92] "Pheophytin.a"                       
##  [93] "Phosphorus..Total."                 
##  [94] "Silica..SiO2...Dissolved."          
##  [95] "Simazine"                           
##  [96] "Solids..Total.Dissolved."           
##  [97] "Solids..Total.Suspended."           
##  [98] "Solids..Volatile.Suspended."        
##  [99] "Thiobencarb"                        
## [100] "Toxaphene"                          
## [101] "Unknown.hydrocarbon"                
## [102] "Zinc..Dissolved."                   
## [103] "Zinc..Total."

#Let's first subset the data Water Years 2005-2012 (October 1, 2004 and ended on September 30, 2012)
BayDeltaWQ$Date <- ymd(BayDeltaWQ$SampleDate)
wtr_yr <- function(x) {
  offset = ifelse(month(x) >= 10, 1, 0)
  adj.year = year(x) + offset
  adj.year
}

BayDeltaWQ$Water_Year <- wtr_yr(BayDeltaWQ$Date)

WQ <- subset(BayDeltaWQ, Water_Year >= 2005 & Water_Year <= 2012 )
# Double check if we get the desired dataset
range(WQ$Water_Year)

## [1] 2005 2012

range(as.character(WQ$SampleDate))

## [1] "2004-10-18" "2012-09-11"

range(WQ$Date)

## [1] "2004-10-18" "2012-09-11"

#Add two columns: year, month
WQ$year <- year(WQ$Date)
WQ$month <- month(WQ$Date)
#I would like to delete the columns with all NAs and then select the water quality variables that I can calculate the mean monthly value since they do not make sense in this analysis.
WQ2 <- WQ[colSums(!is.na(WQ)) > 0]
names(WQ2)

##  [1] "X"                             "SampleDate"                   
##  [3] "StationCode"                   "Depth"                        
##  [5] "Conductance..EC."              "SiteDepth"                    
##  [7] "Field.Notes"                   "Fluorescence"                 
##  [9] "Latitude"                      "Longitude"                    
## [11] "Oxygen"                        "pH"                           
## [13] "Secchi.Depth"                  "Temperature"                  
## [15] "Turbidity"                     "VarType"                      
## [17] "Ammonia..Dissolved."           "Calcium..Dissolved."          
## [19] "Chloride..Dissolved."          "Chlorophyll.a"                
## [21] "Kjeldahl.Nitrogen..Total."     "Nitrite...Nitrate..Dissolved."
## [23] "Organic.Carbon..Dissolved."    "Organic.Carbon..Total."       
## [25] "Organic.Nitrogen..Dissolved."  "Ortho.phosphate..Dissolved."  
## [27] "Pheophytin.a"                  "Phosphorus..Total."           
## [29] "Silica..SiO2...Dissolved."     "Solids..Total.Dissolved."     
## [31] "Solids..Total.Suspended."      "Solids..Volatile.Suspended."  
## [33] "Date"                          "Water_Year"                   
## [35] "year"                          "month"

WQ2 <- WQ2[,-c(1:3,7,16,33:34)]
WQ2$Depth <- as.numeric(as.character(WQ2$Depth))

## Warning: NAs introduced by coercion

test <- WQ2[complete.cases(WQ2),]
#There is no observation if I remove the observations with any NAs. Let's see how many NAs each variable has
NA_Num <- data.frame(sapply(WQ2, function(x) sum(is.na(x))))

#Aggregate to mean monthly data
WQ3<- WQ2 %>%
    group_by(year,month)%>%
    summarise_all(funs(mean(., na.rm=TRUE)))
NA_Num <- data.frame(sapply(WQ3, function(x) sum(is.na(x))))
#subset to delete the variables that contains NA
WQ3 <- subset(WQ3, select=colMeans(is.na(WQ3)) == 0)
# OK! WQ3 is my final dataset! Let's take a look
range(WQ3$year)

## [1] 2004 2012

names(WQ3)

##  [1] "year"                          "month"                        
##  [3] "Depth"                         "Conductance..EC."             
##  [5] "SiteDepth"                     "Fluorescence"                 
##  [7] "Oxygen"                        "Secchi.Depth"                 
##  [9] "Temperature"                   "Turbidity"                    
## [11] "Ammonia..Dissolved."           "Chloride..Dissolved."         
## [13] "Chlorophyll.a"                 "Kjeldahl.Nitrogen..Total."    
## [15] "Nitrite...Nitrate..Dissolved." "Organic.Nitrogen..Dissolved." 
## [17] "Ortho.phosphate..Dissolved."   "Pheophytin.a"                 
## [19] "Phosphorus..Total."            "Silica..SiO2...Dissolved."    
## [21] "Solids..Total.Dissolved."      "Solids..Total.Suspended."     
## [23] "Solids..Volatile.Suspended."

save(WQ3,file="WQ3.rda")

Step 2: Identify variables that are highly correlated with the others

What is Chl-a concentration? BayDeltaWQ$Chlorophyll.a https://www.epa.gov/national-aquatic-resource-surveys/indicators-chlorophyll

#Delete two columns: year and month. And move the Chlorophyll.a to be the first column
Water <- WQ3[,-(1:2)]%>%
  select(Chlorophyll.a, everything())
a <- cor(Water)

## Warning in cor(Water): the standard deviation is zero

unique(Water$Depth)

## [1] 3

#Delete the variable "Depth" since the standard deviation is zero (all the values are 3)
Water <- Water[,-2]
names(Water)

##  [1] "Chlorophyll.a"                 "Conductance..EC."             
##  [3] "SiteDepth"                     "Fluorescence"                 
##  [5] "Oxygen"                        "Secchi.Depth"                 
##  [7] "Temperature"                   "Turbidity"                    
##  [9] "Ammonia..Dissolved."           "Chloride..Dissolved."         
## [11] "Kjeldahl.Nitrogen..Total."     "Nitrite...Nitrate..Dissolved."
## [13] "Organic.Nitrogen..Dissolved."  "Ortho.phosphate..Dissolved."  
## [15] "Pheophytin.a"                  "Phosphorus..Total."           
## [17] "Silica..SiO2...Dissolved."     "Solids..Total.Dissolved."     
## [19] "Solids..Total.Suspended."      "Solids..Volatile.Suspended."

Save for the future! (Some of my thought, like data transformation that I didn’t do in this analysis…)

Take a look at the data WQ3\(Chlorophyll.a. The data is normally distributed after log transformation. plot(density(WQ3\)Chlorophyll.a)) plot(density(log(WQ3\(Chlorophyll.a))) qqnorm(WQ3\)Chlorophyll.a);qqline(WQ3\(Chlorophyll.a) qqnorm(log(WQ3\)Chlorophyll.a));qqline(log(WQ3$Chlorophyll.a))

P <- apply(Water,2, function(col)cor(col, Water$Chlorophyll.a,method = “pearson”))

K <- apply(Water,2, function(col)cor(col, Water$Chlorophyll.a,method = “kendall”))

S <- apply(Water,2, function(col)cor(col, Water$Chlorophyll.a,method = “spearman”))

P_cor <- cor(Water,method = “pearson”) K_cor <- cor(Water,method = “kendall”) S_cor <- cor(Water,method = “spearman”)

# A correlation between -1.0 to -0.5 or 0.5 to 1.0 means that variables are highly correlated.
Fun_corr <- function(x, y) {
  z <- upper.tri(x)
  data.frame(
    row = rownames(x)[row(x)[z]],
    column = rownames(x)[col(x)[z]],
    cor = x[z],
    p = y[z]
    )
}
library(Hmisc)

## Loading required package: lattice

## Loading required package: survival

## Loading required package: Formula

## 
## Attaching package: 'Hmisc'

## The following objects are masked from 'package:dplyr':
## 
##     src, summarize

## The following objects are masked from 'package:base':
## 
##     format.pval, units

cor_water <-rcorr(as.matrix(Water),type="spearman") #rcorr type should be one of “pearson”, “spearman”. I will go with the nonparamertic method "spearman" and keep with further analysis for consistency
test <- Fun_corr(cor_water$r, cor_water$P) 

High_cor <- subset(test, abs(cor) >= 0.5)
High_cor  #High_cor shows the variables that are highly correlated to others

#Chlorophyll.a is highly correlated with Temperature (cor: 0.6003798,P: 1.009286e-10),Ammonia..Dissolved.(cor:-0.5393164,P:1.433183e-08) and Pheophytin.a (cor: 0.7016413, P:1.776357e-15). 
cor(Water$Temperature,Water$Pheophytin.a)

## [1] 0.3554389

#0.3554389 
cor(Water$Temperature,Water$Ammonia..Dissolved.)

## [1] -0.6195209

#-0.6195209
cor(Water$Pheophytin.a,Water$Ammonia..Dissolved.)

## [1] -0.1262

#-0.1262
#There are correlations among Temperature, Pheophytin.a. and Ammonia..Dissolved.Let's do a partial correlation with 4 variables Chlorophyll.a, Temperature, Pheophytin.a. and Ammonia..Dissolved.
model_data <- dplyr::select(Water, Chlorophyll.a, Temperature, Pheophytin.a, Ammonia..Dissolved.)
save(model_data,file="model_data.rda")
require(ppcor)

## Loading required package: ppcor

## Loading required package: MASS

## 
## Attaching package: 'MASS'

## The following object is masked from 'package:dplyr':
## 
##     select

mypcor <- pcor(model_data, method = "spearman")
mycor <- cor(model_data, method = "spearman")
require(corrplot)

## Loading required package: corrplot

## corrplot 0.84 loaded

corrplot(mycor, method = "number")

#Conclusion: Much of the apparent correlation between Chlorophyll.a and Temperature is explained by the mutual negative correlation with Ammonia..Dissolved..Pheophytin.a and Ammonia..Dissolved. should be the best predictors of Chlorophyll.a.

Step 3: develop a predictive model of the mean monthly Chl-a concentration

I developed the predictive models in two ways.

1. Develop a model with variables that were highly correlated with Chlorophyll.a. Based on previous correlation analysis, Pheophytin.a and Ammonia..Dissolved. should be the best predictors of Chlorophyll.a. My null model (lm.null)is that every value is predicted by the mean. The other three models are:lm.C.P which only use Pheophytin.a to predict Chlorophyll.a; lm.C.A which only use Ammonia..Dissolved. to predict Chlorophyll.a; lm.C.A.P which use both Ammonia..Dissolved. and Pheophytin.a to predict Chlorophyll.a.

Results 1: Since the modelthat use both Ammonia..Dissolved. and Pheophytin.a to predict Chlorophyll.a. has the lowest AIC and BIC value, I would choose this model!

2. Do a step model with all the variables that are available to develop the model.

Result 2: I selected the model lm(formula = Chlorophyll.a ~ Conductance..EC. + Oxygen + Temperature + Ammonia..Dissolved. + Kjeldahl.Nitrogen..Total. + Organic.Nitrogen..Dissolved. + Pheophytin.a + Solids..Total.Dissolved., data = Water) that has the lowest AIC value.

Develop model with highly correlated variables

lm.null <- lm(Chlorophyll.a ~ 1, data = model_data); summary(lm.null)

## 
## Call:
## lm(formula = Chlorophyll.a ~ 1, data = model_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.2403 -1.7221 -0.5629  0.8110 11.1228 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   3.7024     0.2352   15.74   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.304 on 95 degrees of freedom

lm.C.P <- lm(Chlorophyll.a ~ Pheophytin.a, data = model_data); summary(lm.C.P)

## 
## Call:
## lm(formula = Chlorophyll.a ~ Pheophytin.a, data = model_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.9290 -0.9760 -0.3091  0.6186 10.1213 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.4458     0.4902   0.909    0.365    
## Pheophytin.a   1.9083     0.2648   7.206 1.43e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.859 on 94 degrees of freedom
## Multiple R-squared:  0.3558, Adjusted R-squared:  0.349 
## F-statistic: 51.92 on 1 and 94 DF,  p-value: 1.426e-10

lm.C.A <- lm(Chlorophyll.a ~ Ammonia..Dissolved., data = model_data); summary(lm.C.A )

## 
## Call:
## lm(formula = Chlorophyll.a ~ Ammonia..Dissolved., data = model_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.0279 -1.3781 -0.4280  0.6737 10.6385 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           5.5981     0.4801  11.660  < 2e-16 ***
## Ammonia..Dissolved. -19.0305     4.3085  -4.417 2.68e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.108 on 94 degrees of freedom
## Multiple R-squared:  0.1719, Adjusted R-squared:  0.1631 
## F-statistic: 19.51 on 1 and 94 DF,  p-value: 2.676e-05

lm.C.A.P <- lm(Chlorophyll.a ~ Ammonia..Dissolved. + Pheophytin.a, data = model_data); summary(lm.C.A.P)

## 
## Call:
## lm(formula = Chlorophyll.a ~ Ammonia..Dissolved. + Pheophytin.a, 
##     data = model_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.2230 -0.8212 -0.3439  0.4131  9.7916 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           2.2600     0.5985   3.776 0.000281 ***
## Ammonia..Dissolved. -15.8271     3.4840  -4.543 1.66e-05 ***
## Pheophytin.a          1.7691     0.2428   7.286 1.02e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.691 on 93 degrees of freedom
## Multiple R-squared:  0.4728, Adjusted R-squared:  0.4615 
## F-statistic:  41.7 on 2 and 93 DF,  p-value: 1.179e-13

require(tidyverse)
require(broom)

## Loading required package: broom

lms <- list(null=lm.null, C.P = lm.C.P, C.A = lm.C.A, C.A.P = lm.C.A.P)
lms.stats <- mapply(glance, lms)
colnames(lms.stats) <- names(lms)
lms.stats

##               null      C.P          C.A          C.A.P     
## r.squared     0         0.3558155    0.1718766    0.4728041 
## adj.r.squared 0         0.3489624    0.1630668    0.4614666 
## sigma         2.304473  1.859407     2.108225     1.691133  
## statistic     NA        51.92092     19.50966     41.70251  
## p.value       NA        1.426426e-10 2.675906e-05 1.1795e-13
## df            1         2            2            3         
## logLik        -215.8612 -194.7523    -206.8088    -185.1325 
## AIC           435.7225  395.5046     419.6176     378.2649  
## BIC           440.8512  403.1976     427.3106     388.5223  
## deviance      504.5064  324.9952     417.7935     265.9737  
## df.residual   95        94           94           93

lms.coeffs <- lapply(lms, tidy)
lms.coeffs

## $null
##          term estimate std.error statistic      p.value
## 1 (Intercept) 3.702413 0.2351992   15.7416 3.222966e-28
## 
## $C.P
##           term  estimate std.error statistic      p.value
## 1  (Intercept) 0.4458041 0.4901807 0.9094689 3.654287e-01
## 2 Pheophytin.a 1.9082623 0.2648298 7.2056171 1.426426e-10
## 
## $C.A
##                  term   estimate std.error statistic      p.value
## 1         (Intercept)   5.598127 0.4801049 11.660216 5.815140e-20
## 2 Ammonia..Dissolved. -19.030521 4.3084976 -4.416974 2.675906e-05
## 
## $C.A.P
##                  term   estimate std.error statistic      p.value
## 1         (Intercept)   2.259966 0.5985250  3.775893 2.807757e-04
## 2 Ammonia..Dissolved. -15.827065 3.4839587 -4.542839 1.663622e-05
## 3        Pheophytin.a   1.769061 0.2428043  7.285954 1.020820e-10

lms.coeffs.notalist <- Map(cbind, lms.coeffs, model = names(lms))
lms.coeffs.notalist <- bind_rows(lms.coeffs.notalist)

## Warning in bind_rows_(x, .id): Unequal factor levels: coercing to character

## Warning in bind_rows_(x, .id): binding character and factor vector,
## coercing into character vector

## Warning in bind_rows_(x, .id): binding character and factor vector,
## coercing into character vector

## Warning in bind_rows_(x, .id): binding character and factor vector,
## coercing into character vector

## Warning in bind_rows_(x, .id): binding character and factor vector,
## coercing into character vector

lms.coeffs.notalist

unlist(lms.stats["adj.r.squared",])

##      null       C.P       C.A     C.A.P 
## 0.0000000 0.3489624 0.1630668 0.4614666

aic <- as.data.frame(unlist(lms.stats["AIC",]))
colnames(aic) <- "AIC"
aic

bic <- as.data.frame(unlist(lms.stats["BIC",]))
colnames(bic) <- "BIC"
bic

aic.bic <- cbind(aic,bic)
a.b <- aic.bic %>% 
  rownames_to_column() %>% 
  gather(metric, value, -rowname) %>% 
  ggplot(aes(rowname, value, fill = metric)) +
  geom_bar(position = "dodge", stat = "identity")
a.b

# The modelthat use both Ammonia..Dissolved. and Pheophytin.a to predict Chlorophyll.a. has the lowest AIC and BIC value

Step model

lms <- step(lm(Chlorophyll.a ~ ., data = Water))

## Start:  AIC=107.15
## Chlorophyll.a ~ Conductance..EC. + SiteDepth + Fluorescence + 
##     Oxygen + Secchi.Depth + Temperature + Turbidity + Ammonia..Dissolved. + 
##     Chloride..Dissolved. + Kjeldahl.Nitrogen..Total. + Nitrite...Nitrate..Dissolved. + 
##     Organic.Nitrogen..Dissolved. + Ortho.phosphate..Dissolved. + 
##     Pheophytin.a + Phosphorus..Total. + Silica..SiO2...Dissolved. + 
##     Solids..Total.Dissolved. + Solids..Total.Suspended. + Solids..Volatile.Suspended.
## 
##                                 Df Sum of Sq    RSS    AIC
## - Chloride..Dissolved.           1    0.1053 193.32 105.20
## - Silica..SiO2...Dissolved.      1    0.1530 193.37 105.22
## - SiteDepth                      1    0.1873 193.40 105.24
## - Solids..Volatile.Suspended.    1    0.4308 193.65 105.36
## - Secchi.Depth                   1    0.4332 193.65 105.36
## - Fluorescence                   1    1.2865 194.50 105.78
## - Nitrite...Nitrate..Dissolved.  1    1.3820 194.60 105.83
## - Solids..Total.Dissolved.       1    1.8177 195.03 106.05
## - Solids..Total.Suspended.       1    2.8941 196.11 106.58
## - Phosphorus..Total.             1    2.9108 196.13 106.58
## - Ortho.phosphate..Dissolved.    1    3.0721 196.29 106.66
## - Turbidity                      1    3.4363 196.65 106.84
## <none>                                       193.22 107.15
## - Conductance..EC.               1    5.3139 198.53 107.75
## - Organic.Nitrogen..Dissolved.   1    6.9628 200.18 108.55
## - Ammonia..Dissolved.            1    7.1268 200.34 108.62
## - Kjeldahl.Nitrogen..Total.      1   14.2855 207.50 112.00
## - Pheophytin.a                   1   21.2346 214.45 115.16
## - Oxygen                         1   24.4146 217.63 116.57
## - Temperature                    1   30.4240 223.64 119.19
## 
## Step:  AIC=105.2
## Chlorophyll.a ~ Conductance..EC. + SiteDepth + Fluorescence + 
##     Oxygen + Secchi.Depth + Temperature + Turbidity + Ammonia..Dissolved. + 
##     Kjeldahl.Nitrogen..Total. + Nitrite...Nitrate..Dissolved. + 
##     Organic.Nitrogen..Dissolved. + Ortho.phosphate..Dissolved. + 
##     Pheophytin.a + Phosphorus..Total. + Silica..SiO2...Dissolved. + 
##     Solids..Total.Dissolved. + Solids..Total.Suspended. + Solids..Volatile.Suspended.
## 
##                                 Df Sum of Sq    RSS    AIC
## - Silica..SiO2...Dissolved.      1    0.1592 193.48 103.28
## - SiteDepth                      1    0.1968 193.52 103.30
## - Secchi.Depth                   1    0.4396 193.76 103.42
## - Solids..Volatile.Suspended.    1    0.5469 193.87 103.47
## - Fluorescence                   1    1.2836 194.60 103.84
## - Nitrite...Nitrate..Dissolved.  1    1.3566 194.68 103.87
## - Phosphorus..Total.             1    2.8668 196.19 104.61
## - Ortho.phosphate..Dissolved.    1    3.0540 196.38 104.70
## - Solids..Total.Suspended.       1    3.3110 196.63 104.83
## - Turbidity                      1    3.6032 196.92 104.97
## <none>                                       193.32 105.20
## - Conductance..EC.               1    5.2441 198.56 105.77
## - Organic.Nitrogen..Dissolved.   1    6.9384 200.26 106.58
## - Ammonia..Dissolved.            1    7.1861 200.51 106.70
## - Solids..Total.Dissolved.       1    7.5245 200.84 106.87
## - Kjeldahl.Nitrogen..Total.      1   14.2241 207.54 110.02
## - Pheophytin.a                   1   21.4009 214.72 113.28
## - Oxygen                         1   24.4635 217.78 114.64
## - Temperature                    1   30.4330 223.75 117.23
## 
## Step:  AIC=103.28
## Chlorophyll.a ~ Conductance..EC. + SiteDepth + Fluorescence + 
##     Oxygen + Secchi.Depth + Temperature + Turbidity + Ammonia..Dissolved. + 
##     Kjeldahl.Nitrogen..Total. + Nitrite...Nitrate..Dissolved. + 
##     Organic.Nitrogen..Dissolved. + Ortho.phosphate..Dissolved. + 
##     Pheophytin.a + Phosphorus..Total. + Solids..Total.Dissolved. + 
##     Solids..Total.Suspended. + Solids..Volatile.Suspended.
## 
##                                 Df Sum of Sq    RSS    AIC
## - SiteDepth                      1    0.2766 193.76 101.42
## - Secchi.Depth                   1    0.3914 193.87 101.47
## - Solids..Volatile.Suspended.    1    0.4895 193.97 101.52
## - Fluorescence                   1    1.1959 194.68 101.87
## - Nitrite...Nitrate..Dissolved.  1    1.4999 194.98 102.02
## - Solids..Total.Suspended.       1    3.1773 196.66 102.84
## - Phosphorus..Total.             1    3.1842 196.66 102.85
## - Ortho.phosphate..Dissolved.    1    3.2539 196.73 102.88
## - Turbidity                      1    3.5444 197.02 103.02
## <none>                                       193.48 103.28
## - Conductance..EC.               1    5.4099 198.89 103.93
## - Organic.Nitrogen..Dissolved.   1    7.0822 200.56 104.73
## - Ammonia..Dissolved.            1    7.1799 200.66 104.78
## - Solids..Total.Dissolved.       1    8.1623 201.64 105.25
## - Kjeldahl.Nitrogen..Total.      1   14.2840 207.76 108.12
## - Pheophytin.a                   1   21.8176 215.30 111.54
## - Oxygen                         1   24.6432 218.12 112.79
## - Temperature                    1   30.9407 224.42 115.52
## 
## Step:  AIC=101.42
## Chlorophyll.a ~ Conductance..EC. + Fluorescence + Oxygen + Secchi.Depth + 
##     Temperature + Turbidity + Ammonia..Dissolved. + Kjeldahl.Nitrogen..Total. + 
##     Nitrite...Nitrate..Dissolved. + Organic.Nitrogen..Dissolved. + 
##     Ortho.phosphate..Dissolved. + Pheophytin.a + Phosphorus..Total. + 
##     Solids..Total.Dissolved. + Solids..Total.Suspended. + Solids..Volatile.Suspended.
## 
##                                 Df Sum of Sq    RSS     AIC
## - Solids..Volatile.Suspended.    1    0.3585 194.12  99.594
## - Secchi.Depth                   1    0.3807 194.14  99.605
## - Fluorescence                   1    1.1985 194.96 100.008
## - Nitrite...Nitrate..Dissolved.  1    1.4433 195.20 100.129
## - Phosphorus..Total.             1    2.9718 196.73 100.878
## - Solids..Total.Suspended.       1    3.1076 196.86 100.944
## - Ortho.phosphate..Dissolved.    1    3.1374 196.89 100.958
## - Turbidity                      1    3.9862 197.74 101.371
## <none>                                       193.76 101.416
## - Conductance..EC.               1    5.1485 198.91 101.934
## - Organic.Nitrogen..Dissolved.   1    6.8907 200.65 102.771
## - Ammonia..Dissolved.            1    6.9174 200.67 102.784
## - Solids..Total.Dissolved.       1    8.0373 201.79 103.318
## - Kjeldahl.Nitrogen..Total.      1   14.0195 207.78 106.123
## - Pheophytin.a                   1   21.9835 215.74 109.734
## - Oxygen                         1   24.6628 218.42 110.919
## - Temperature                    1   30.9562 224.71 113.646
## 
## Step:  AIC=99.59
## Chlorophyll.a ~ Conductance..EC. + Fluorescence + Oxygen + Secchi.Depth + 
##     Temperature + Turbidity + Ammonia..Dissolved. + Kjeldahl.Nitrogen..Total. + 
##     Nitrite...Nitrate..Dissolved. + Organic.Nitrogen..Dissolved. + 
##     Ortho.phosphate..Dissolved. + Pheophytin.a + Phosphorus..Total. + 
##     Solids..Total.Dissolved. + Solids..Total.Suspended.
## 
##                                 Df Sum of Sq    RSS     AIC
## - Secchi.Depth                   1    0.6084 194.72  97.894
## - Fluorescence                   1    1.0496 195.16  98.112
## - Nitrite...Nitrate..Dissolved.  1    1.5339 195.65  98.349
## - Phosphorus..Total.             1    3.0474 197.16  99.089
## - Solids..Total.Suspended.       1    3.3241 197.44  99.224
## - Ortho.phosphate..Dissolved.    1    3.4619 197.58  99.291
## - Turbidity                      1    3.9120 198.03  99.509
## <none>                                       194.12  99.594
## - Conductance..EC.               1    5.4754 199.59 100.264
## - Organic.Nitrogen..Dissolved.   1    6.9837 201.10 100.987
## - Ammonia..Dissolved.            1    7.0997 201.22 101.042
## - Solids..Total.Dissolved.       1    8.6806 202.80 101.794
## - Kjeldahl.Nitrogen..Total.      1   13.9597 208.07 104.261
## - Pheophytin.a                   1   22.1308 216.25 107.958
## - Oxygen                         1   25.1256 219.24 109.279
## - Temperature                    1   31.0355 225.15 111.832
## 
## Step:  AIC=97.89
## Chlorophyll.a ~ Conductance..EC. + Fluorescence + Oxygen + Temperature + 
##     Turbidity + Ammonia..Dissolved. + Kjeldahl.Nitrogen..Total. + 
##     Nitrite...Nitrate..Dissolved. + Organic.Nitrogen..Dissolved. + 
##     Ortho.phosphate..Dissolved. + Pheophytin.a + Phosphorus..Total. + 
##     Solids..Total.Dissolved. + Solids..Total.Suspended.
## 
##                                 Df Sum of Sq    RSS     AIC
## - Fluorescence                   1    1.7386 196.46  96.748
## - Nitrite...Nitrate..Dissolved.  1    1.7911 196.51  96.773
## - Phosphorus..Total.             1    3.3417 198.06  97.528
## - Turbidity                      1    3.4827 198.21  97.596
## - Ortho.phosphate..Dissolved.    1    3.6162 198.34  97.661
## - Solids..Total.Suspended.       1    4.0758 198.80  97.883
## <none>                                       194.72  97.894
## - Conductance..EC.               1    4.9090 199.63  98.284
## - Organic.Nitrogen..Dissolved.   1    7.4152 202.14  99.482
## - Ammonia..Dissolved.            1    7.9918 202.72  99.756
## - Solids..Total.Dissolved.       1    8.4141 203.14  99.955
## - Kjeldahl.Nitrogen..Total.      1   15.0990 209.82 103.064
## - Pheophytin.a                   1   21.6069 216.33 105.996
## - Oxygen                         1   24.5395 219.26 107.289
## - Temperature                    1   30.4470 225.17 109.841
## 
## Step:  AIC=96.75
## Chlorophyll.a ~ Conductance..EC. + Oxygen + Temperature + Turbidity + 
##     Ammonia..Dissolved. + Kjeldahl.Nitrogen..Total. + Nitrite...Nitrate..Dissolved. + 
##     Organic.Nitrogen..Dissolved. + Ortho.phosphate..Dissolved. + 
##     Pheophytin.a + Phosphorus..Total. + Solids..Total.Dissolved. + 
##     Solids..Total.Suspended.
## 
##                                 Df Sum of Sq    RSS     AIC
## - Nitrite...Nitrate..Dissolved.  1     1.826 198.29  95.636
## - Phosphorus..Total.             1     3.273 199.74  96.334
## - Ortho.phosphate..Dissolved.    1     3.565 200.03  96.474
## - Solids..Total.Suspended.       1     3.598 200.06  96.490
## - Conductance..EC.               1     3.798 200.26  96.586
## <none>                                       196.46  96.748
## - Turbidity                      1     4.796 201.26  97.063
## - Solids..Total.Dissolved.       1     7.343 203.81  98.270
## - Organic.Nitrogen..Dissolved.   1     8.003 204.47  98.581
## - Ammonia..Dissolved.            1     8.537 205.00  98.831
## - Kjeldahl.Nitrogen..Total.      1    15.371 211.83 101.979
## - Pheophytin.a                   1    23.105 219.57 105.422
## - Oxygen                         1    30.273 226.74 108.506
## - Temperature                    1    34.768 231.23 110.390
## 
## Step:  AIC=95.64
## Chlorophyll.a ~ Conductance..EC. + Oxygen + Temperature + Turbidity + 
##     Ammonia..Dissolved. + Kjeldahl.Nitrogen..Total. + Organic.Nitrogen..Dissolved. + 
##     Ortho.phosphate..Dissolved. + Pheophytin.a + Phosphorus..Total. + 
##     Solids..Total.Dissolved. + Solids..Total.Suspended.
## 
##                                Df Sum of Sq    RSS     AIC
## - Ortho.phosphate..Dissolved.   1     2.019 200.31  94.609
## - Phosphorus..Total.            1     2.357 200.65  94.770
## - Solids..Total.Suspended.      1     2.987 201.28  95.071
## <none>                                      198.29  95.636
## - Turbidity                     1     4.198 202.49  95.647
## - Conductance..EC.              1     4.256 202.54  95.675
## - Solids..Total.Dissolved.      1     6.420 204.71  96.695
## - Ammonia..Dissolved.           1     8.847 207.13  97.826
## - Organic.Nitrogen..Dissolved.  1     9.402 207.69  98.083
## - Kjeldahl.Nitrogen..Total.     1    13.679 211.97 100.040
## - Pheophytin.a                  1    21.447 219.74 103.495
## - Oxygen                        1    28.539 226.83 106.545
## - Temperature                   1    36.698 234.99 109.937
## 
## Step:  AIC=94.61
## Chlorophyll.a ~ Conductance..EC. + Oxygen + Temperature + Turbidity + 
##     Ammonia..Dissolved. + Kjeldahl.Nitrogen..Total. + Organic.Nitrogen..Dissolved. + 
##     Pheophytin.a + Phosphorus..Total. + Solids..Total.Dissolved. + 
##     Solids..Total.Suspended.
## 
##                                Df Sum of Sq    RSS     AIC
## - Phosphorus..Total.            1     0.672 200.98  92.930
## - Solids..Total.Suspended.      1     3.746 204.05  94.387
## - Turbidity                     1     3.751 204.06  94.390
## - Conductance..EC.              1     4.209 204.52  94.605
## <none>                                      200.31  94.609
## - Solids..Total.Dissolved.      1     7.068 207.38  95.938
## - Ammonia..Dissolved.           1     7.441 207.75  96.110
## - Organic.Nitrogen..Dissolved.  1     7.789 208.10  96.271
## - Kjeldahl.Nitrogen..Total.     1    13.454 213.76  98.849
## - Pheophytin.a                  1    20.260 220.57 101.858
## - Oxygen                        1    27.227 227.53 104.844
## - Temperature                   1    37.488 237.79 109.078
## 
## Step:  AIC=92.93
## Chlorophyll.a ~ Conductance..EC. + Oxygen + Temperature + Turbidity + 
##     Ammonia..Dissolved. + Kjeldahl.Nitrogen..Total. + Organic.Nitrogen..Dissolved. + 
##     Pheophytin.a + Solids..Total.Dissolved. + Solids..Total.Suspended.
## 
##                                Df Sum of Sq    RSS     AIC
## - Turbidity                     1     3.100 204.08  92.400
## - Solids..Total.Suspended.      1     3.963 204.94  92.805
## <none>                                      200.98  92.930
## - Conductance..EC.              1     4.927 205.91  93.255
## - Solids..Total.Dissolved.      1     7.269 208.25  94.341
## - Ammonia..Dissolved.           1     7.779 208.76  94.576
## - Organic.Nitrogen..Dissolved.  1     8.014 208.99  94.684
## - Kjeldahl.Nitrogen..Total.     1    14.551 215.53  97.640
## - Pheophytin.a                  1    19.967 220.95 100.023
## - Oxygen                        1    27.201 228.18 103.116
## - Temperature                   1    36.898 237.88 107.111
## 
## Step:  AIC=92.4
## Chlorophyll.a ~ Conductance..EC. + Oxygen + Temperature + Ammonia..Dissolved. + 
##     Kjeldahl.Nitrogen..Total. + Organic.Nitrogen..Dissolved. + 
##     Pheophytin.a + Solids..Total.Dissolved. + Solids..Total.Suspended.
## 
##                                Df Sum of Sq    RSS     AIC
## - Solids..Total.Suspended.      1     1.256 205.34  90.989
## <none>                                      204.08  92.400
## - Solids..Total.Dissolved.      1     5.504 209.58  92.954
## - Conductance..EC.              1     5.935 210.01  93.152
## - Organic.Nitrogen..Dissolved.  1     6.604 210.68  93.457
## - Ammonia..Dissolved.           1     7.142 211.22  93.702
## - Kjeldahl.Nitrogen..Total.     1    15.495 219.57  97.425
## - Pheophytin.a                  1    19.519 223.60  99.168
## - Oxygen                        1    24.199 228.28 101.157
## - Temperature                   1    33.812 237.89 105.117
## 
## Step:  AIC=90.99
## Chlorophyll.a ~ Conductance..EC. + Oxygen + Temperature + Ammonia..Dissolved. + 
##     Kjeldahl.Nitrogen..Total. + Organic.Nitrogen..Dissolved. + 
##     Pheophytin.a + Solids..Total.Dissolved.
## 
##                                Df Sum of Sq    RSS     AIC
## <none>                                      205.34  90.989
## - Organic.Nitrogen..Dissolved.  1     5.636 210.97  91.588
## - Ammonia..Dissolved.           1     5.937 211.27  91.725
## - Conductance..EC.              1     7.110 212.45  92.257
## - Solids..Total.Dissolved.      1     7.239 212.57  92.315
## - Kjeldahl.Nitrogen..Total.     1    14.382 219.72  95.488
## - Pheophytin.a                  1    18.560 223.90  97.296
## - Oxygen                        1    29.235 234.57 101.767
## - Temperature                   1    39.524 244.86 105.888

final.mod <- stepAIC(lms)

## Start:  AIC=90.99
## Chlorophyll.a ~ Conductance..EC. + Oxygen + Temperature + Ammonia..Dissolved. + 
##     Kjeldahl.Nitrogen..Total. + Organic.Nitrogen..Dissolved. + 
##     Pheophytin.a + Solids..Total.Dissolved.
## 
##                                Df Sum of Sq    RSS     AIC
## <none>                                      205.34  90.989
## - Organic.Nitrogen..Dissolved.  1     5.636 210.97  91.588
## - Ammonia..Dissolved.           1     5.937 211.27  91.725
## - Conductance..EC.              1     7.110 212.45  92.257
## - Solids..Total.Dissolved.      1     7.239 212.57  92.315
## - Kjeldahl.Nitrogen..Total.     1    14.382 219.72  95.488
## - Pheophytin.a                  1    18.560 223.90  97.296
## - Oxygen                        1    29.235 234.57 101.767
## - Temperature                   1    39.524 244.86 105.888

Step 4: Final model selection My final model: lm(formula = Chlorophyll.a ~ Conductance..EC. + Oxygen + Temperature + Ammonia..Dissolved. + Kjeldahl.Nitrogen..Total. + Organic.Nitrogen..Dissolved. + Pheophytin.a + Solids..Total.Dissolved., data = Water) Diagnostic Plots analysis: (1)Residual plots indicate that both models meet the regression assumptions very well. (2)From the Q-Q plots we can see residuals are Normally distributed. Observations numbered as 57 and 45 are extreme values. (3)From Scale-Location plots, final.mod model perfoms better because it has a horizontal line with equally (randomly) spread points. (4)Residuals vs Leverage plots help us to find influential cases.The plot identified the influential observation as #15. If I exclude the 15th case from the analysis, the slope coefficient and R2 would change. From the analysis above, I will go with the final.mod model. Let’s take a look at the comparasion of predicted values and the actual values.

Reference:https://www.statmethods.net/stats/rdiagnostics.html https://onlinecourses.science.psu.edu/stat501/node/36 http://data.library.virginia.edu/diagnostic-plots/

#First, take a look at the results.
summary(final.mod)

## 
## Call:
## lm(formula = Chlorophyll.a ~ Conductance..EC. + Oxygen + Temperature + 
##     Ammonia..Dissolved. + Kjeldahl.Nitrogen..Total. + Organic.Nitrogen..Dissolved. + 
##     Pheophytin.a + Solids..Total.Dissolved., data = Water)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.5837 -0.7604 -0.1729  0.5220  8.1688 
## 
## Coefficients:
##                                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                  -2.818e+01  7.968e+00  -3.536 0.000653 ***
## Conductance..EC.             -3.190e-04  1.838e-04  -1.736 0.086158 .  
## Oxygen                        2.288e+00  6.500e-01   3.519 0.000690 ***
## Temperature                   5.800e-01  1.417e-01   4.092 9.52e-05 ***
## Ammonia..Dissolved.          -8.995e+00  5.672e+00  -1.586 0.116359    
## Kjeldahl.Nitrogen..Total.     6.765e+00  2.741e+00   2.469 0.015522 *  
## Organic.Nitrogen..Dissolved. -4.271e+00  2.764e+00  -1.545 0.125911    
## Pheophytin.a                  8.332e-01  2.971e-01   2.804 0.006219 ** 
## Solids..Total.Dissolved.      5.821e-04  3.324e-04   1.751 0.083415 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.536 on 87 degrees of freedom
## Multiple R-squared:  0.593,  Adjusted R-squared:  0.5556 
## F-statistic: 15.84 on 8 and 87 DF,  p-value: 3.569e-14

summary(lm.C.A.P)

## 
## Call:
## lm(formula = Chlorophyll.a ~ Ammonia..Dissolved. + Pheophytin.a, 
##     data = model_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.2230 -0.8212 -0.3439  0.4131  9.7916 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           2.2600     0.5985   3.776 0.000281 ***
## Ammonia..Dissolved. -15.8271     3.4840  -4.543 1.66e-05 ***
## Pheophytin.a          1.7691     0.2428   7.286 1.02e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.691 on 93 degrees of freedom
## Multiple R-squared:  0.4728, Adjusted R-squared:  0.4615 
## F-statistic:  41.7 on 2 and 93 DF,  p-value: 1.179e-13

#final.mod has a higher value of R-square (0.593) compared with lm.C.A.P (0.4728).

layout(matrix(c(1,2,3,4),2,2))
plot(final.mod)

plot(lm.C.A.P)

Water$predicted <- predict(final.mod)   # Save the predicted values
Water$residuals <- residuals(final.mod)
plot(Water$Chlorophyll.a, Water$predicted,
      xlab="actual", ylab="predicted")
 abline(a=0,b=1)
save(Water,file="Water.rda")

Step 5: Quantify how much variance in mean monthly Chl-a is explained by the variable selected. Results: 59.3% variance in mean monthly Chl-a is explained by the variable selected. Pheophytin.a has the highest relative importance

Reference: https://stats.stackexchange.com/questions/79399/calculate-variance-explained-by-each-predictor-in-multiple-regression-using-r

summary(final.mod)

## 
## Call:
## lm(formula = Chlorophyll.a ~ Conductance..EC. + Oxygen + Temperature + 
##     Ammonia..Dissolved. + Kjeldahl.Nitrogen..Total. + Organic.Nitrogen..Dissolved. + 
##     Pheophytin.a + Solids..Total.Dissolved., data = Water)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.5837 -0.7604 -0.1729  0.5220  8.1688 
## 
## Coefficients:
##                                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                  -2.818e+01  7.968e+00  -3.536 0.000653 ***
## Conductance..EC.             -3.190e-04  1.838e-04  -1.736 0.086158 .  
## Oxygen                        2.288e+00  6.500e-01   3.519 0.000690 ***
## Temperature                   5.800e-01  1.417e-01   4.092 9.52e-05 ***
## Ammonia..Dissolved.          -8.995e+00  5.672e+00  -1.586 0.116359    
## Kjeldahl.Nitrogen..Total.     6.765e+00  2.741e+00   2.469 0.015522 *  
## Organic.Nitrogen..Dissolved. -4.271e+00  2.764e+00  -1.545 0.125911    
## Pheophytin.a                  8.332e-01  2.971e-01   2.804 0.006219 ** 
## Solids..Total.Dissolved.      5.821e-04  3.324e-04   1.751 0.083415 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.536 on 87 degrees of freedom
## Multiple R-squared:  0.593,  Adjusted R-squared:  0.5556 
## F-statistic: 15.84 on 8 and 87 DF,  p-value: 3.569e-14

#R-square is the percentage of the response variable variation that is explained by the variable selected. In this model R-square is 0.593 which means that 59.3% variance in mean monthly Chl-a is explained by the variable selected.

#Take a look at the relative importance of the variables.
library(relaimpo)

## Loading required package: boot

## 
## Attaching package: 'boot'

## The following object is masked from 'package:survival':
## 
##     aml

## The following object is masked from 'package:lattice':
## 
##     melanoma

## Loading required package: survey

## Loading required package: grid

## Loading required package: Matrix

## 
## Attaching package: 'Matrix'

## The following object is masked from 'package:tidyr':
## 
##     expand

## 
## Attaching package: 'survey'

## The following object is masked from 'package:Hmisc':
## 
##     deff

## The following object is masked from 'package:graphics':
## 
##     dotchart

## Loading required package: mitools

## This is the global version of package relaimpo.

## If you are a non-US user, a version with the interesting additional metric pmvd is available

## from Ulrike Groempings web site at prof.beuth-hochschule.de/groemping.

calc.relimp(final.mod,type=c("lmg","last","first","pratt"),
   rela=TRUE)

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Response variable: Chlorophyll.a 
## Total response variance: 5.310594 
## Analysis based on 96 observations 
## 
## 8 Regressors: 
## Conductance..EC. Oxygen Temperature Ammonia..Dissolved. Kjeldahl.Nitrogen..Total. Organic.Nitrogen..Dissolved. Pheophytin.a Solids..Total.Dissolved. 
## Proportion of variance explained by model: 59.3%
## Metrics are normalized to sum to 100% (rela=TRUE). 
## 
## Relative importance metrics: 
## 
##                                     lmg       last      first      pratt
## Conductance..EC.             0.05037311 0.05571372 0.04105362  0.1615399
## Oxygen                       0.12591509 0.22907045 0.07116362 -0.3551473
## Temperature                  0.28491928 0.30969191 0.25498100  0.9612862
## Ammonia..Dissolved.          0.10891972 0.04652015 0.16886981  0.1370017
## Kjeldahl.Nitrogen..Total.    0.04090709 0.11269311 0.04686570 -0.1391048
## Organic.Nitrogen..Dissolved. 0.02858313 0.04415933 0.05001446  0.0769623
## Pheophytin.a                 0.32864816 0.14543018 0.34959080  0.2619794
## Solids..Total.Dissolved.     0.03173443 0.05672116 0.01746099 -0.1045174
## 
## Average coefficients for different model sizes: 
## 
##                                         1X           2Xs           3Xs
## Conductance..EC.             -1.391459e-04 -2.094920e-04 -2.654653e-04
## Oxygen                       -7.868286e-01 -9.717217e-02  5.125043e-01
## Temperature                   2.640627e-01  3.307760e-01  4.004268e-01
## Ammonia..Dissolved.          -1.903052e+01 -1.674643e+01 -1.432084e+01
## Kjeldahl.Nitrogen..Total.    -3.912077e+00 -1.516564e+00  6.780462e-01
## Organic.Nitrogen..Dissolved. -4.763903e+00 -2.788569e+00 -1.907726e+00
## Pheophytin.a                  1.908262e+00  1.795168e+00  1.681185e+00
## Solids..Total.Dissolved.     -1.669013e-04  2.142197e-05  1.995030e-04
##                                        4Xs           5Xs           6Xs
## Conductance..EC.             -2.950923e-04 -3.007668e-04 -2.954979e-04
## Oxygen                        1.055305e+00  1.514735e+00  1.878921e+00
## Temperature                   4.607603e-01  5.089229e-01  5.451188e-01
## Ammonia..Dissolved.          -1.239616e+01 -1.111321e+01 -1.028165e+01
## Kjeldahl.Nitrogen..Total.     2.476014e+00  3.857562e+00  4.966139e+00
## Organic.Nitrogen..Dissolved. -1.893868e+00 -2.231158e+00 -2.751341e+00
## Pheophytin.a                  1.553192e+00  1.404428e+00  1.233285e+00
## Solids..Total.Dissolved.      3.366624e-04  4.247183e-04  4.769126e-04
##                                        7Xs           8Xs
## Conductance..EC.             -0.0002962846 -0.0003189970
## Oxygen                        2.1387672698  2.2878017652
## Temperature                   0.5694142558  0.5800155254
## Ammonia..Dissolved.          -9.6075010776 -8.9952345079
## Kjeldahl.Nitrogen..Total.     5.9092666616  6.7652229218
## Organic.Nitrogen..Dissolved. -3.4285546533 -4.2710349150
## Pheophytin.a                  1.0392422788  0.8331687493
## Solids..Total.Dissolved.      0.0005190703  0.0005820596

# Bootstrap Measures of Relative Importance (1000 samples) 
boot <- boot.relimp(final.mod, b = 1000, type = c("lmg", 
  "last", "first", "pratt"), rank = TRUE, 
  diff = TRUE, rela = TRUE)

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

booteval.relimp(boot) # print result

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

## Response variable: Chlorophyll.a 
## Total response variance: 5.310594 
## Analysis based on 96 observations 
## 
## 8 Regressors: 
## Conductance..EC. Oxygen Temperature Ammonia..Dissolved. Kjeldahl.Nitrogen..Total. Organic.Nitrogen..Dissolved. Pheophytin.a Solids..Total.Dissolved. 
## Proportion of variance explained by model: 59.3%
## Metrics are normalized to sum to 100% (rela=TRUE). 
## 
## Relative importance metrics: 
## 
##                                     lmg       last      first      pratt
## Conductance..EC.             0.05037311 0.05571372 0.04105362  0.1615399
## Oxygen                       0.12591509 0.22907045 0.07116362 -0.3551473
## Temperature                  0.28491928 0.30969191 0.25498100  0.9612862
## Ammonia..Dissolved.          0.10891972 0.04652015 0.16886981  0.1370017
## Kjeldahl.Nitrogen..Total.    0.04090709 0.11269311 0.04686570 -0.1391048
## Organic.Nitrogen..Dissolved. 0.02858313 0.04415933 0.05001446  0.0769623
## Pheophytin.a                 0.32864816 0.14543018 0.34959080  0.2619794
## Solids..Total.Dissolved.     0.03173443 0.05672116 0.01746099 -0.1045174
## 
## Average coefficients for different model sizes: 
## 
##                                         1X           2Xs           3Xs
## Conductance..EC.             -1.391459e-04 -2.094920e-04 -2.654653e-04
## Oxygen                       -7.868286e-01 -9.717217e-02  5.125043e-01
## Temperature                   2.640627e-01  3.307760e-01  4.004268e-01
## Ammonia..Dissolved.          -1.903052e+01 -1.674643e+01 -1.432084e+01
## Kjeldahl.Nitrogen..Total.    -3.912077e+00 -1.516564e+00  6.780462e-01
## Organic.Nitrogen..Dissolved. -4.763903e+00 -2.788569e+00 -1.907726e+00
## Pheophytin.a                  1.908262e+00  1.795168e+00  1.681185e+00
## Solids..Total.Dissolved.     -1.669013e-04  2.142197e-05  1.995030e-04
##                                        4Xs           5Xs           6Xs
## Conductance..EC.             -2.950923e-04 -3.007668e-04 -2.954979e-04
## Oxygen                        1.055305e+00  1.514735e+00  1.878921e+00
## Temperature                   4.607603e-01  5.089229e-01  5.451188e-01
## Ammonia..Dissolved.          -1.239616e+01 -1.111321e+01 -1.028165e+01
## Kjeldahl.Nitrogen..Total.     2.476014e+00  3.857562e+00  4.966139e+00
## Organic.Nitrogen..Dissolved. -1.893868e+00 -2.231158e+00 -2.751341e+00
## Pheophytin.a                  1.553192e+00  1.404428e+00  1.233285e+00
## Solids..Total.Dissolved.      3.366624e-04  4.247183e-04  4.769126e-04
##                                        7Xs           8Xs
## Conductance..EC.             -0.0002962846 -0.0003189970
## Oxygen                        2.1387672698  2.2878017652
## Temperature                   0.5694142558  0.5800155254
## Ammonia..Dissolved.          -9.6075010776 -8.9952345079
## Kjeldahl.Nitrogen..Total.     5.9092666616  6.7652229218
## Organic.Nitrogen..Dissolved. -3.4285546533 -4.2710349150
## Pheophytin.a                  1.0392422788  0.8331687493
## Solids..Total.Dissolved.      0.0005190703  0.0005820596
## 
##  
##  Confidence interval information ( 1000 bootstrap replicates, bty= perc ): 
## Relative Contributions with confidence intervals: 
##  
##                                                        Lower  Upper
##                                    percentage 0.95     0.95    0.95   
## Conductance..EC..lmg                0.0504    __CDEFGH  0.0111  0.1569
## Oxygen.lmg                          0.1259    __CDE___  0.0823  0.1712
## Temperature.lmg                     0.2849    AB______  0.1936  0.3451
## Ammonia..Dissolved..lmg             0.1089    __CDEF__  0.0621  0.1892
## Kjeldahl.Nitrogen..Total..lmg       0.0409    ____EFGH  0.0234  0.0843
## Organic.Nitrogen..Dissolved..lmg    0.0286    ____EFGH  0.0102  0.0665
## Pheophytin.a.lmg                    0.3286    AB______  0.1803  0.4829
## Solids..Total.Dissolved..lmg        0.0317    ___DEFGH  0.0088  0.1068
##                                                                       
## Conductance..EC..last               0.0557    ABCDEFGH  0.0001  0.2825
## Oxygen.last                         0.2291    ABCDEFGH  0.0284  0.4120
## Temperature.last                    0.3097    ABCDEFG_  0.0426  0.4911
## Ammonia..Dissolved..last            0.0465    _BCDEFGH  0.0004  0.2180
## Kjeldahl.Nitrogen..Total..last      0.1127    ABCDEFG_  0.0020  0.2518
## Organic.Nitrogen..Dissolved..last   0.0442    ___DEFGH  0.0000  0.1503
## Pheophytin.a.last                   0.1454    ABCDEFGH  0.0059  0.4827
## Solids..Total.Dissolved..last       0.0567    ABCDEFGH  0.0001  0.2652
##                                                                       
## Conductance..EC..first              0.0411    ___DEFG_  0.0027  0.1236
## Oxygen.first                        0.0712    ___DEFGH  0.0120  0.1297
## Temperature.first                   0.2550    ABC_____  0.1690  0.2991
## Ammonia..Dissolved..first           0.1689    _BC_____  0.1165  0.2318
## Kjeldahl.Nitrogen..Total..first     0.0469    ___DEFGH  0.0067  0.1113
## Organic.Nitrogen..Dissolved..first  0.0500    ___DEFGH  0.0074  0.1011
## Pheophytin.a.first                  0.3496    ABC_____  0.2056  0.5078
## Solids..Total.Dissolved..first      0.0175    ____EFGH  0.0001  0.0824
##                                                                       
## Conductance..EC..pratt              0.1615    _BCDEFG_ -0.1454  0.5735
## Oxygen.pratt                       -0.3551    ______GH -0.6066 -0.0920
## Temperature.pratt                   0.9613    AB______  0.3857  1.4197
## Ammonia..Dissolved..pratt           0.1370    _BCDE___  0.0087  0.4162
## Kjeldahl.Nitrogen..Total..pratt    -0.1391    ____EFGH -0.2901 -0.0132
## Organic.Nitrogen..Dissolved..pratt  0.0770    __CDEF__ -0.0502  0.2080
## Pheophytin.a.pratt                  0.2620    ABCDE___  0.0537  0.5319
## Solids..Total.Dissolved..pratt     -0.1045    __CDEFGH -0.3702  0.1128
## 
## Letters indicate the ranks covered by bootstrap CIs. 
## (Rank bootstrap confidence intervals always obtained by percentile method) 
## CAUTION: Bootstrap confidence intervals can be somewhat liberal. 
## 
##  
##  Differences between Relative Contributions: 
##  
##                                                                              Lower   Upper
##                                                              difference
## Conductance..EC.-Oxygen.lmg                                  -0.0755   
## Conductance..EC.-Temperature.lmg                             -0.2345   
## Conductance..EC.-Ammonia..Dissolved..lmg                     -0.0585   
## Conductance..EC.-Kjeldahl.Nitrogen..Total..lmg                0.0095   
## Conductance..EC.-Organic.Nitrogen..Dissolved..lmg             0.0218   
## Conductance..EC.-Pheophytin.a.lmg                            -0.2783   
## Conductance..EC.-Solids..Total.Dissolved..lmg                 0.0186   
## Oxygen-Temperature.lmg                                       -0.1590   
## Oxygen-Ammonia..Dissolved..lmg                                0.0170   
## Oxygen-Kjeldahl.Nitrogen..Total..lmg                          0.0850   
## Oxygen-Organic.Nitrogen..Dissolved..lmg                       0.0973   
## Oxygen-Pheophytin.a.lmg                                      -0.2027   
## Oxygen-Solids..Total.Dissolved..lmg                           0.0942   
## Temperature-Ammonia..Dissolved..lmg                           0.1760   
## Temperature-Kjeldahl.Nitrogen..Total..lmg                     0.2440   
## Temperature-Organic.Nitrogen..Dissolved..lmg                  0.2563   
## Temperature-Pheophytin.a.lmg                                 -0.0437   
## Temperature-Solids..Total.Dissolved..lmg                      0.2532   
## Ammonia..Dissolved.-Kjeldahl.Nitrogen..Total..lmg             0.0680   
## Ammonia..Dissolved.-Organic.Nitrogen..Dissolved..lmg          0.0803   
## Ammonia..Dissolved.-Pheophytin.a.lmg                         -0.2197   
## Ammonia..Dissolved.-Solids..Total.Dissolved..lmg              0.0772   
## Kjeldahl.Nitrogen..Total.-Organic.Nitrogen..Dissolved..lmg    0.0123   
## Kjeldahl.Nitrogen..Total.-Pheophytin.a.lmg                   -0.2877   
## Kjeldahl.Nitrogen..Total.-Solids..Total.Dissolved..lmg        0.0092   
## Organic.Nitrogen..Dissolved.-Pheophytin.a.lmg                -0.3001   
## Organic.Nitrogen..Dissolved.-Solids..Total.Dissolved..lmg    -0.0032   
## Pheophytin.a-Solids..Total.Dissolved..lmg                     0.2969   
##                                                                        
## Conductance..EC.-Oxygen.last                                 -0.1734   
## Conductance..EC.-Temperature.last                            -0.2540   
## Conductance..EC.-Ammonia..Dissolved..last                     0.0092   
## Conductance..EC.-Kjeldahl.Nitrogen..Total..last              -0.0570   
## Conductance..EC.-Organic.Nitrogen..Dissolved..last            0.0116   
## Conductance..EC.-Pheophytin.a.last                           -0.0897   
## Conductance..EC.-Solids..Total.Dissolved..last               -0.0010   
## Oxygen-Temperature.last                                      -0.0806   
## Oxygen-Ammonia..Dissolved..last                               0.1826   
## Oxygen-Kjeldahl.Nitrogen..Total..last                         0.1164   
## Oxygen-Organic.Nitrogen..Dissolved..last                      0.1849   
## Oxygen-Pheophytin.a.last                                      0.0836   
## Oxygen-Solids..Total.Dissolved..last                          0.1723   
## Temperature-Ammonia..Dissolved..last                          0.2632   
## Temperature-Kjeldahl.Nitrogen..Total..last                    0.1970   
## Temperature-Organic.Nitrogen..Dissolved..last                 0.2655   
## Temperature-Pheophytin.a.last                                 0.1643   
## Temperature-Solids..Total.Dissolved..last                     0.2530   
## Ammonia..Dissolved.-Kjeldahl.Nitrogen..Total..last           -0.0662   
## Ammonia..Dissolved.-Organic.Nitrogen..Dissolved..last         0.0024   
## Ammonia..Dissolved.-Pheophytin.a.last                        -0.0989   
## Ammonia..Dissolved.-Solids..Total.Dissolved..last            -0.0102   
## Kjeldahl.Nitrogen..Total.-Organic.Nitrogen..Dissolved..last   0.0685   
## Kjeldahl.Nitrogen..Total.-Pheophytin.a.last                  -0.0327   
## Kjeldahl.Nitrogen..Total.-Solids..Total.Dissolved..last       0.0560   
## Organic.Nitrogen..Dissolved.-Pheophytin.a.last               -0.1013   
## Organic.Nitrogen..Dissolved.-Solids..Total.Dissolved..last   -0.0126   
## Pheophytin.a-Solids..Total.Dissolved..last                    0.0887   
##                                                                        
## Conductance..EC.-Oxygen.first                                -0.0301   
## Conductance..EC.-Temperature.first                           -0.2139   
## Conductance..EC.-Ammonia..Dissolved..first                   -0.1278   
## Conductance..EC.-Kjeldahl.Nitrogen..Total..first             -0.0058   
## Conductance..EC.-Organic.Nitrogen..Dissolved..first          -0.0090   
## Conductance..EC.-Pheophytin.a.first                          -0.3085   
## Conductance..EC.-Solids..Total.Dissolved..first               0.0236   
## Oxygen-Temperature.first                                     -0.1838   
## Oxygen-Ammonia..Dissolved..first                             -0.0977   
## Oxygen-Kjeldahl.Nitrogen..Total..first                        0.0243   
## Oxygen-Organic.Nitrogen..Dissolved..first                     0.0211   
## Oxygen-Pheophytin.a.first                                    -0.2784   
## Oxygen-Solids..Total.Dissolved..first                         0.0537   
## Temperature-Ammonia..Dissolved..first                         0.0861   
## Temperature-Kjeldahl.Nitrogen..Total..first                   0.2081   
## Temperature-Organic.Nitrogen..Dissolved..first                0.2050   
## Temperature-Pheophytin.a.first                               -0.0946   
## Temperature-Solids..Total.Dissolved..first                    0.2375   
## Ammonia..Dissolved.-Kjeldahl.Nitrogen..Total..first           0.1220   
## Ammonia..Dissolved.-Organic.Nitrogen..Dissolved..first        0.1189   
## Ammonia..Dissolved.-Pheophytin.a.first                       -0.1807   
## Ammonia..Dissolved.-Solids..Total.Dissolved..first            0.1514   
## Kjeldahl.Nitrogen..Total.-Organic.Nitrogen..Dissolved..first -0.0031   
## Kjeldahl.Nitrogen..Total.-Pheophytin.a.first                 -0.3027   
## Kjeldahl.Nitrogen..Total.-Solids..Total.Dissolved..first      0.0294   
## Organic.Nitrogen..Dissolved.-Pheophytin.a.first              -0.2996   
## Organic.Nitrogen..Dissolved.-Solids..Total.Dissolved..first   0.0326   
## Pheophytin.a-Solids..Total.Dissolved..first                   0.3321   
##                                                                        
## Conductance..EC.-Oxygen.pratt                                 0.5167   
## Conductance..EC.-Temperature.pratt                           -0.7997   
## Conductance..EC.-Ammonia..Dissolved..pratt                    0.0245   
## Conductance..EC.-Kjeldahl.Nitrogen..Total..pratt              0.3006   
## Conductance..EC.-Organic.Nitrogen..Dissolved..pratt           0.0846   
## Conductance..EC.-Pheophytin.a.pratt                          -0.1004   
## Conductance..EC.-Solids..Total.Dissolved..pratt               0.2661   
## Oxygen-Temperature.pratt                                     -1.3164   
## Oxygen-Ammonia..Dissolved..pratt                             -0.4921   
## Oxygen-Kjeldahl.Nitrogen..Total..pratt                       -0.2160   
## Oxygen-Organic.Nitrogen..Dissolved..pratt                    -0.4321   
## Oxygen-Pheophytin.a.pratt                                    -0.6171   
## Oxygen-Solids..Total.Dissolved..pratt                        -0.2506   
## Temperature-Ammonia..Dissolved..pratt                         0.8243   
## Temperature-Kjeldahl.Nitrogen..Total..pratt                   1.1004   
## Temperature-Organic.Nitrogen..Dissolved..pratt                0.8843   
## Temperature-Pheophytin.a.pratt                                0.6993   
## Temperature-Solids..Total.Dissolved..pratt                    1.0658   
## Ammonia..Dissolved.-Kjeldahl.Nitrogen..Total..pratt           0.2761   
## Ammonia..Dissolved.-Organic.Nitrogen..Dissolved..pratt        0.0600   
## Ammonia..Dissolved.-Pheophytin.a.pratt                       -0.1250   
## Ammonia..Dissolved.-Solids..Total.Dissolved..pratt            0.2415   
## Kjeldahl.Nitrogen..Total.-Organic.Nitrogen..Dissolved..pratt -0.2161   
## Kjeldahl.Nitrogen..Total.-Pheophytin.a.pratt                 -0.4011   
## Kjeldahl.Nitrogen..Total.-Solids..Total.Dissolved..pratt     -0.0346   
## Organic.Nitrogen..Dissolved.-Pheophytin.a.pratt              -0.1850   
## Organic.Nitrogen..Dissolved.-Solids..Total.Dissolved..pratt   0.1815   
## Pheophytin.a-Solids..Total.Dissolved..pratt                   0.3665   
##                                                              0.95 0.95   
## Conductance..EC.-Oxygen.lmg                                       -0.1491
## Conductance..EC.-Temperature.lmg                              *   -0.3198
## Conductance..EC.-Ammonia..Dissolved..lmg                          -0.1623
## Conductance..EC.-Kjeldahl.Nitrogen..Total..lmg                    -0.0535
## Conductance..EC.-Organic.Nitrogen..Dissolved..lmg                 -0.0279
## Conductance..EC.-Pheophytin.a.lmg                             *   -0.4618
## Conductance..EC.-Solids..Total.Dissolved..lmg                     -0.0009
## Oxygen-Temperature.lmg                                        *   -0.1930
## Oxygen-Ammonia..Dissolved..lmg                                    -0.0757
## Oxygen-Kjeldahl.Nitrogen..Total..lmg                          *    0.0175
## Oxygen-Organic.Nitrogen..Dissolved..lmg                       *    0.0301
## Oxygen-Pheophytin.a.lmg                                       *   -0.3781
## Oxygen-Solids..Total.Dissolved..lmg                               -0.0108
## Temperature-Ammonia..Dissolved..lmg                           *    0.0474
## Temperature-Kjeldahl.Nitrogen..Total..lmg                     *    0.1285
## Temperature-Organic.Nitrogen..Dissolved..lmg                  *    0.1475
## Temperature-Pheophytin.a.lmg                                      -0.2589
## Temperature-Solids..Total.Dissolved..lmg                      *    0.1019
## Ammonia..Dissolved.-Kjeldahl.Nitrogen..Total..lmg             *    0.0086
## Ammonia..Dissolved.-Organic.Nitrogen..Dissolved..lmg          *    0.0112
## Ammonia..Dissolved.-Pheophytin.a.lmg                          *   -0.3906
## Ammonia..Dissolved.-Solids..Total.Dissolved..lmg                  -0.0272
## Kjeldahl.Nitrogen..Total.-Organic.Nitrogen..Dissolved..lmg        -0.0106
## Kjeldahl.Nitrogen..Total.-Pheophytin.a.lmg                    *   -0.4534
## Kjeldahl.Nitrogen..Total.-Solids..Total.Dissolved..lmg            -0.0631
## Organic.Nitrogen..Dissolved.-Pheophytin.a.lmg                 *   -0.4650
## Organic.Nitrogen..Dissolved.-Solids..Total.Dissolved..lmg         -0.0752
## Pheophytin.a-Solids..Total.Dissolved..lmg                     *    0.0952
##                                                                          
## Conductance..EC.-Oxygen.last                                      -0.4056
## Conductance..EC.-Temperature.last                                 -0.4846
## Conductance..EC.-Ammonia..Dissolved..last                         -0.1952
## Conductance..EC.-Kjeldahl.Nitrogen..Total..last                   -0.2143
## Conductance..EC.-Organic.Nitrogen..Dissolved..last                -0.0860
## Conductance..EC.-Pheophytin.a.last                                -0.4701
## Conductance..EC.-Solids..Total.Dissolved..last                    -0.0470
## Oxygen-Temperature.last                                           -0.1605
## Oxygen-Ammonia..Dissolved..last                                   -0.1298
## Oxygen-Kjeldahl.Nitrogen..Total..last                             -0.1826
## Oxygen-Organic.Nitrogen..Dissolved..last                          -0.0777
## Oxygen-Pheophytin.a.last                                          -0.3728
## Oxygen-Solids..Total.Dissolved..last                              -0.2128
## Temperature-Ammonia..Dissolved..last                              -0.1341
## Temperature-Kjeldahl.Nitrogen..Total..last                        -0.1556
## Temperature-Organic.Nitrogen..Dissolved..last                     -0.0575
## Temperature-Pheophytin.a.last                                     -0.3684
## Temperature-Solids..Total.Dissolved..last                         -0.1775
## Ammonia..Dissolved.-Kjeldahl.Nitrogen..Total..last                -0.1753
## Ammonia..Dissolved.-Organic.Nitrogen..Dissolved..last             -0.1050
## Ammonia..Dissolved.-Pheophytin.a.last                             -0.4122
## Ammonia..Dissolved.-Solids..Total.Dissolved..last                 -0.2435
## Kjeldahl.Nitrogen..Total.-Organic.Nitrogen..Dissolved..last       -0.0184
## Kjeldahl.Nitrogen..Total.-Pheophytin.a.last                       -0.4423
## Kjeldahl.Nitrogen..Total.-Solids..Total.Dissolved..last           -0.1925
## Organic.Nitrogen..Dissolved.-Pheophytin.a.last                    -0.4795
## Organic.Nitrogen..Dissolved.-Solids..Total.Dissolved..last        -0.2170
## Pheophytin.a-Solids..Total.Dissolved..last                        -0.2131
##                                                                          
## Conductance..EC.-Oxygen.first                                     -0.1122
## Conductance..EC.-Temperature.first                            *   -0.2869
## Conductance..EC.-Ammonia..Dissolved..first                    *   -0.2023
## Conductance..EC.-Kjeldahl.Nitrogen..Total..first                  -0.0818
## Conductance..EC.-Organic.Nitrogen..Dissolved..first               -0.0817
## Conductance..EC.-Pheophytin.a.first                           *   -0.4885
## Conductance..EC.-Solids..Total.Dissolved..first                   -0.0012
## Oxygen-Temperature.first                                      *   -0.2209
## Oxygen-Ammonia..Dissolved..first                              *   -0.1894
## Oxygen-Kjeldahl.Nitrogen..Total..first                            -0.0737
## Oxygen-Organic.Nitrogen..Dissolved..first                         -0.0608
## Oxygen-Pheophytin.a.first                                     *   -0.4508
## Oxygen-Solids..Total.Dissolved..first                             -0.0614
## Temperature-Ammonia..Dissolved..first                             -0.0161
## Temperature-Kjeldahl.Nitrogen..Total..first                   *    0.0895
## Temperature-Organic.Nitrogen..Dissolved..first                *    0.1055
## Temperature-Pheophytin.a.first                                    -0.2832
## Temperature-Solids..Total.Dissolved..first                    *    0.1018
## Ammonia..Dissolved.-Kjeldahl.Nitrogen..Total..first           *    0.0483
## Ammonia..Dissolved.-Organic.Nitrogen..Dissolved..first        *    0.0438
## Ammonia..Dissolved.-Pheophytin.a.first                            -0.3815
## Ammonia..Dissolved.-Solids..Total.Dissolved..first            *    0.0739
## Kjeldahl.Nitrogen..Total.-Organic.Nitrogen..Dissolved..first      -0.0460
## Kjeldahl.Nitrogen..Total.-Pheophytin.a.first                  *   -0.4921
## Kjeldahl.Nitrogen..Total.-Solids..Total.Dissolved..first          -0.0466
## Organic.Nitrogen..Dissolved.-Pheophytin.a.first               *   -0.4865
## Organic.Nitrogen..Dissolved.-Solids..Total.Dissolved..first       -0.0582
## Pheophytin.a-Solids..Total.Dissolved..first                   *    0.1627
##                                                                          
## Conductance..EC.-Oxygen.pratt                                 *    0.0417
## Conductance..EC.-Temperature.pratt                            *   -1.4480
## Conductance..EC.-Ammonia..Dissolved..pratt                        -0.4668
## Conductance..EC.-Kjeldahl.Nitrogen..Total..pratt                  -0.0965
## Conductance..EC.-Organic.Nitrogen..Dissolved..pratt               -0.1574
## Conductance..EC.-Pheophytin.a.pratt                               -0.6250
## Conductance..EC.-Solids..Total.Dissolved..pratt                   -0.2547
## Oxygen-Temperature.pratt                                      *   -2.0256
## Oxygen-Ammonia..Dissolved..pratt                              *   -0.8062
## Oxygen-Kjeldahl.Nitrogen..Total..pratt                            -0.4857
## Oxygen-Organic.Nitrogen..Dissolved..pratt                     *   -0.6904
## Oxygen-Pheophytin.a.pratt                                     *   -0.8583
## Oxygen-Solids..Total.Dissolved..pratt                             -0.6251
## Temperature-Ammonia..Dissolved..pratt                         *    0.0637
## Temperature-Kjeldahl.Nitrogen..Total..pratt                   *    0.4697
## Temperature-Organic.Nitrogen..Dissolved..pratt                *    0.2994
## Temperature-Pheophytin.a.pratt                                    -0.1011
## Temperature-Solids..Total.Dissolved..pratt                    *    0.4141
## Ammonia..Dissolved.-Kjeldahl.Nitrogen..Total..pratt           *    0.0535
## Ammonia..Dissolved.-Organic.Nitrogen..Dissolved..pratt            -0.0913
## Ammonia..Dissolved.-Pheophytin.a.pratt                            -0.3926
## Ammonia..Dissolved.-Solids..Total.Dissolved..pratt                -0.0333
## Kjeldahl.Nitrogen..Total.-Organic.Nitrogen..Dissolved..pratt      -0.4835
## Kjeldahl.Nitrogen..Total.-Pheophytin.a.pratt                  *   -0.6449
## Kjeldahl.Nitrogen..Total.-Solids..Total.Dissolved..pratt          -0.2599
## Organic.Nitrogen..Dissolved.-Pheophytin.a.pratt                   -0.5296
## Organic.Nitrogen..Dissolved.-Solids..Total.Dissolved..pratt       -0.1251
## Pheophytin.a-Solids..Total.Dissolved..pratt                   *    0.1082
##                                                              0.95   
## Conductance..EC.-Oxygen.lmg                                   0.0616
## Conductance..EC.-Temperature.lmg                             -0.0625
## Conductance..EC.-Ammonia..Dissolved..lmg                      0.0694
## Conductance..EC.-Kjeldahl.Nitrogen..Total..lmg                0.1164
## Conductance..EC.-Organic.Nitrogen..Dissolved..lmg             0.1176
## Conductance..EC.-Pheophytin.a.lmg                            -0.0552
## Conductance..EC.-Solids..Total.Dissolved..lmg                 0.0550
## Oxygen-Temperature.lmg                                       -0.0920
## Oxygen-Ammonia..Dissolved..lmg                                0.0763
## Oxygen-Kjeldahl.Nitrogen..Total..lmg                          0.1317
## Oxygen-Organic.Nitrogen..Dissolved..lmg                       0.1473
## Oxygen-Pheophytin.a.lmg                                      -0.0354
## Oxygen-Solids..Total.Dissolved..lmg                           0.1529
## Temperature-Ammonia..Dissolved..lmg                           0.2389
## Temperature-Kjeldahl.Nitrogen..Total..lmg                     0.3060
## Temperature-Organic.Nitrogen..Dissolved..lmg                  0.3193
## Temperature-Pheophytin.a.lmg                                  0.1270
## Temperature-Solids..Total.Dissolved..lmg                      0.3231
## Ammonia..Dissolved.-Kjeldahl.Nitrogen..Total..lmg             0.1382
## Ammonia..Dissolved.-Organic.Nitrogen..Dissolved..lmg          0.1630
## Ammonia..Dissolved.-Pheophytin.a.lmg                         -0.0276
## Ammonia..Dissolved.-Solids..Total.Dissolved..lmg              0.1679
## Kjeldahl.Nitrogen..Total.-Organic.Nitrogen..Dissolved..lmg    0.0474
## Kjeldahl.Nitrogen..Total.-Pheophytin.a.lmg                   -0.1154
## Kjeldahl.Nitrogen..Total.-Solids..Total.Dissolved..lmg        0.0569
## Organic.Nitrogen..Dissolved.-Pheophytin.a.lmg                -0.1291
## Organic.Nitrogen..Dissolved.-Solids..Total.Dissolved..lmg     0.0322
## Pheophytin.a-Solids..Total.Dissolved..lmg                     0.4651
##                                                                     
## Conductance..EC.-Oxygen.last                                  0.2185
## Conductance..EC.-Temperature.last                             0.1895
## Conductance..EC.-Ammonia..Dissolved..last                     0.2570
## Conductance..EC.-Kjeldahl.Nitrogen..Total..last               0.2057
## Conductance..EC.-Organic.Nitrogen..Dissolved..last            0.2287
## Conductance..EC.-Pheophytin.a.last                            0.2340
## Conductance..EC.-Solids..Total.Dissolved..last                0.0518
## Oxygen-Temperature.last                                       0.0561
## Oxygen-Ammonia..Dissolved..last                               0.4011
## Oxygen-Kjeldahl.Nitrogen..Total..last                         0.3994
## Oxygen-Organic.Nitrogen..Dissolved..last                      0.3991
## Oxygen-Pheophytin.a.last                                      0.3411
## Oxygen-Solids..Total.Dissolved..last                          0.4061
## Temperature-Ammonia..Dissolved..last                          0.4810
## Temperature-Kjeldahl.Nitrogen..Total..last                    0.4798
## Temperature-Organic.Nitrogen..Dissolved..last                 0.4835
## Temperature-Pheophytin.a.last                                 0.4330
## Temperature-Solids..Total.Dissolved..last                     0.4854
## Ammonia..Dissolved.-Kjeldahl.Nitrogen..Total..last            0.1280
## Ammonia..Dissolved.-Organic.Nitrogen..Dissolved..last         0.2028
## Ammonia..Dissolved.-Pheophytin.a.last                         0.0554
## Ammonia..Dissolved.-Solids..Total.Dissolved..last             0.2007
## Kjeldahl.Nitrogen..Total.-Organic.Nitrogen..Dissolved..last   0.1888
## Kjeldahl.Nitrogen..Total.-Pheophytin.a.last                   0.1770
## Kjeldahl.Nitrogen..Total.-Solids..Total.Dissolved..last       0.2126
## Organic.Nitrogen..Dissolved.-Pheophytin.a.last                0.0997
## Organic.Nitrogen..Dissolved.-Solids..Total.Dissolved..last    0.0806
## Pheophytin.a-Solids..Total.Dissolved..last                    0.4738
##                                                                     
## Conductance..EC.-Oxygen.first                                 0.0925
## Conductance..EC.-Temperature.first                           -0.0656
## Conductance..EC.-Ammonia..Dissolved..first                   -0.0322
## Conductance..EC.-Kjeldahl.Nitrogen..Total..first              0.0891
## Conductance..EC.-Organic.Nitrogen..Dissolved..first           0.0898
## Conductance..EC.-Pheophytin.a.first                          -0.1318
## Conductance..EC.-Solids..Total.Dissolved..first               0.0667
## Oxygen-Temperature.first                                     -0.1347
## Oxygen-Ammonia..Dissolved..first                             -0.0095
## Oxygen-Kjeldahl.Nitrogen..Total..first                        0.1028
## Oxygen-Organic.Nitrogen..Dissolved..first                     0.0895
## Oxygen-Pheophytin.a.first                                    -0.1094
## Oxygen-Solids..Total.Dissolved..first                         0.1254
## Temperature-Ammonia..Dissolved..first                         0.1570
## Temperature-Kjeldahl.Nitrogen..Total..first                   0.2699
## Temperature-Organic.Nitrogen..Dissolved..first                0.2635
## Temperature-Pheophytin.a.first                                0.0596
## Temperature-Solids..Total.Dissolved..first                    0.2944
## Ammonia..Dissolved.-Kjeldahl.Nitrogen..Total..first           0.1855
## Ammonia..Dissolved.-Organic.Nitrogen..Dissolved..first        0.1934
## Ammonia..Dissolved.-Pheophytin.a.first                        0.0130
## Ammonia..Dissolved.-Solids..Total.Dissolved..first            0.2112
## Kjeldahl.Nitrogen..Total.-Organic.Nitrogen..Dissolved..first  0.0539
## Kjeldahl.Nitrogen..Total.-Pheophytin.a.first                 -0.1198
## Kjeldahl.Nitrogen..Total.-Solids..Total.Dissolved..first      0.0892
## Organic.Nitrogen..Dissolved.-Pheophytin.a.first              -0.1346
## Organic.Nitrogen..Dissolved.-Solids..Total.Dissolved..first   0.0947
## Pheophytin.a-Solids..Total.Dissolved..first                   0.4984
##                                                                     
## Conductance..EC.-Oxygen.pratt                                 0.8935
## Conductance..EC.-Temperature.pratt                           -0.0278
## Conductance..EC.-Ammonia..Dissolved..pratt                    0.4562
## Conductance..EC.-Kjeldahl.Nitrogen..Total..pratt              0.7247
## Conductance..EC.-Organic.Nitrogen..Dissolved..pratt           0.4864
## Conductance..EC.-Pheophytin.a.pratt                           0.4426
## Conductance..EC.-Solids..Total.Dissolved..pratt               0.9366
## Oxygen-Temperature.pratt                                     -0.4925
## Oxygen-Ammonia..Dissolved..pratt                             -0.2261
## Oxygen-Kjeldahl.Nitrogen..Total..pratt                        0.0159
## Oxygen-Organic.Nitrogen..Dissolved..pratt                    -0.1086
## Oxygen-Pheophytin.a.pratt                                    -0.3422
## Oxygen-Solids..Total.Dissolved..pratt                         0.1453
## Temperature-Ammonia..Dissolved..pratt                         1.3287
## Temperature-Kjeldahl.Nitrogen..Total..pratt                   1.6051
## Temperature-Organic.Nitrogen..Dissolved..pratt                1.3846
## Temperature-Pheophytin.a.pratt                                1.2871
## Temperature-Solids..Total.Dissolved..pratt                    1.4789
## Ammonia..Dissolved.-Kjeldahl.Nitrogen..Total..pratt           0.6291
## Ammonia..Dissolved.-Organic.Nitrogen..Dissolved..pratt        0.3842
## Ammonia..Dissolved.-Pheophytin.a.pratt                        0.1651
## Ammonia..Dissolved.-Solids..Total.Dissolved..pratt            0.5904
## Kjeldahl.Nitrogen..Total.-Organic.Nitrogen..Dissolved..pratt  0.0265
## Kjeldahl.Nitrogen..Total.-Pheophytin.a.pratt                 -0.1836
## Kjeldahl.Nitrogen..Total.-Solids..Total.Dissolved..pratt      0.2558
## Organic.Nitrogen..Dissolved.-Pheophytin.a.pratt               0.1089
## Organic.Nitrogen..Dissolved.-Solids..Total.Dissolved..pratt   0.4769
## Pheophytin.a-Solids..Total.Dissolved..pratt                   0.6339
## 
## * indicates that CI for difference does not include 0. 
## CAUTION: Bootstrap confidence intervals can be somewhat liberal.

layout(matrix(c(1,2,3,4),2,2))
plot(booteval.relimp(boot,sort=TRUE)) # plot result

## Warning in rev(variances[[p]]) - variances[[p + 1]]: Recycling array of length 1 in vector-array arithmetic is deprecated.
##   Use c() or as.vector() instead.

# Results indicate that Pheophytin.a has the highest relative importance.

Question 2: Model the mean monthly Chl-a concentration as a function of season and the water quality variable idenitifed as MOST important in explaining the variance of Chl-a from question 1

Step 1:create a new discrete value called “season”, and assign a label to data for “wet season” and “dry season”. Model the mean monthly Chl-a concentration as a function of season and Pheophytin.a.

Answer: There is no clear defination of dry and wet season for Bay Delta. According to the monthly precipitation in Sacramento from https://www.usclimatedata.com/climate/california/united-states/3174, I will define precipiation equal or larger than 1 inch to be the wet season (Novermber to April) and lower than inch to be the dry season (May to October) in this analysis. 14.72% variation in Chlorophyll.a is explained by season. 35.58% variation in Chlorophyll.a is explained by Pheophytin.a. 40.86% variation in Chlorophyll.a is explained by both season and Pheophytin.a. The combined model is better than individual models. The mean of Chlorophyll.a in dry season is 4.58 while in wet season is 2.82. The slopes of the linear regression after accounting for season are: wet season (-1.0952),Pheophytin.a(1.7). The slope of the linear regression not considering season is Pheophytin.a(1.9083). From the plots we can see residuals are normally distributed (but with several extreme events).

Reference: https://feliperego.github.io/blog/2015/10/23/Interpreting-Model-Output-In-R

WQ3$Season <- ifelse(WQ3$month %in% c(5:10), "DrySeason",
                        "WetSeason"  )
WaterSeason <- dplyr::select(WQ3, Chlorophyll.a, Pheophytin.a, Season)

## Adding missing grouping variables: `year`

WaterSeason$Season <- as.factor(WaterSeason$Season)
save(WaterSeason,file="WaterSeason.rda")

lm.C.S <- lm(Chlorophyll.a ~ Season, data = WaterSeason); summary(lm.C.S)

## 
## Call:
## lm(formula = Chlorophyll.a ~ Season, data = WaterSeason)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.7434 -1.3911 -0.5860  0.9637 10.2433 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       4.5820     0.3088  14.838  < 2e-16 ***
## SeasonWetSeason  -1.7591     0.4367  -4.028 0.000114 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.139 on 94 degrees of freedom
## Multiple R-squared:  0.1472, Adjusted R-squared:  0.1381 
## F-statistic: 16.23 on 1 and 94 DF,  p-value: 0.0001139

lm.C.P <- lm(Chlorophyll.a ~ Pheophytin.a, data = WaterSeason); summary(lm.C.P)

## 
## Call:
## lm(formula = Chlorophyll.a ~ Pheophytin.a, data = WaterSeason)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.9290 -0.9760 -0.3091  0.6186 10.1213 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.4458     0.4902   0.909    0.365    
## Pheophytin.a   1.9083     0.2648   7.206 1.43e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.859 on 94 degrees of freedom
## Multiple R-squared:  0.3558, Adjusted R-squared:  0.349 
## F-statistic: 51.92 on 1 and 94 DF,  p-value: 1.426e-10

lm.C.S.P <- lm(Chlorophyll.a ~ Season + Pheophytin.a, data = WaterSeason); summary(lm.C.S.P)

## 
## Call:
## lm(formula = Chlorophyll.a ~ Season + Pheophytin.a, data = WaterSeason)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.1971 -0.8580 -0.2034  0.6192  9.6830 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       1.3488     0.5667   2.380  0.01934 *  
## SeasonWetSeason  -1.0952     0.3800  -2.882  0.00491 ** 
## Pheophytin.a      1.7000     0.2651   6.412  5.9e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.791 on 93 degrees of freedom
## Multiple R-squared:  0.4086, Adjusted R-squared:  0.3959 
## F-statistic: 32.13 on 2 and 93 DF,  p-value: 2.462e-11

DrySeason <- mean(WaterSeason[WaterSeason$Season %in% "DrySeason",]$Chlorophyll.a)
WetSeason <- mean(WaterSeason[WaterSeason$Season %in% "WetSeason",]$Chlorophyll.a)

plot(lm.C.S.P)

Step 2: Plot Chl-a vs your most important variable, with the observations colored by season. Add the paralell regression lines from the combined model in yellow, and add the univariate regression line in blue.

predicted_df <- data.frame(Chl_pred = predict(lm.C.S.P, WaterSeason), Pheophytin.a = WaterSeason$Pheophytin.a)

ggplot(WaterSeason) +
      geom_point(mapping = aes(x = Pheophytin.a , y = Chlorophyll.a, color = Season)) +
  geom_smooth(method = "lm", mapping = aes(x = Pheophytin.a , y = Chlorophyll.a))+
geom_line(color='yellow',data = predicted_df, aes(x=Pheophytin.a , y= Chl_pred))